Method for measuring fiber orientation degree, fiber orientation degree measurement apparatus, and control computer program for fiber orientation degree measurement apparatus

ABSTRACT

A method for measuring a fiber orientation degree includes: irradiating a sample formed of a composite material containing discontinuous carbon fibers with an X-ray to acquire an X-ray diffraction image; calculating an angle (2θ)A of a peak originating from a crystal face of graphite; calculating a correction coefficient δ of a thickness of the sample; calculating an upper limit (2θ)B of the peak of the crystal face of graphite; calculating a diffraction sensitivity IC(ϕ) of the peak originating from the crystal face of graphite by correcting an integrating range with the correction coefficient δ and integrating the X-ray diffraction image with respect to a diffraction angle (2θ); and calculating a fiber orientation degree Sd(β) by the method of Hermans from the diffraction sensitivity IC(ϕ).

FIELD

The present invention relates to a method for measuring a fiberorientation degree of a composite material containing discontinuouscarbon fibers, a fiber orientation degree measurement apparatus, and acontrol program for a fiber orientation degree measurement apparatus.

BACKGROUND

Carbon fiber reinforced plastics (hereinafter, also called “CFRP”) withimproved strength by blending carbon fibers into plastics are being usedfor various uses. Information on a fiber orientation degree, that is, alevel of presence in each direction at which carbon fibers present inCFRP are present, is important technical information for the propertiesof CFRP and determination of phenomena during molding.

Examples of known means for measuring information on the distribution ofcarbon fibers in CFRP include X-ray computer tomography (CT), X-raytransmission imaging, and microscopic observation of polished surfaces;they have problems in that it takes time for pretreatment andmeasurement apparatuses are expensive.

A method is developed, in which X-ray diffractometry is used, respectiveX-ray diffraction images are acquired for a sample for which theorientation degree is desired to be measured and a control sample inwhich carbon fibers are unidirectionally oriented, crystal orientationdegrees from pieces of diffraction information of the respective samplesare calculated, and a fiber orientation degree of the sample iscalculated by removing the influence of a matrix resin in CFRP from acrystal orientation degree of the sample using a crystal orientationdegree of the control sample (refer to Patent Literature 1, forexample).

CITATION LIST Patent Literature

Patent Literature 1: Japanese Patent Application Laid-open No.2016-90259

SUMMARY Technical Problem

However, in Patent Literature 1, the control sample is required to beprepared, and the orientation degree cannot simply be calculated. Thecrystal orientation degree calculated in Patent Literature 1 is atwo-dimensional (in-plane) crystal orientation degree, in which fiberdistribution in a thickness direction of the sample is not considered,and is difficult to use for a sample in which fiber orientation variesin the thickness direction.

The present invention has been made in view of the above, and an objectthereof is to provide a method for measuring a fiber orientation degree,a fiber orientation degree measurement apparatus, and a control programfor a fiber orientation degree measurement apparatus considering fiberorientation in a thickness direction simply and accurately.

Solution to Problem

To solve the problem described above and to achieve the object, a methodfor measuring a fiber orientation degree according to the presentinvention includes: a diffraction image acquisition process ofirradiating a sample formed of a composite material containingdiscontinuous carbon fibers with an X-ray to acquire an X-raydiffraction image; a peak angle calculation process of calculating anangle (2θ)_(A) of a peak originating from a crystal face of graphitefrom an inflection point A of an integral value I(2θ) obtained byintegrating the X-ray diffraction image with respect to an azimuth angle(ϕ); a correction coefficient calculation process of calculating acorrection coefficient δ of a thickness of the sample; an upper limitcalculation process of calculating an upper limit (2θ)_(B) of the peakof the crystal face of graphite from an inflection point B of theintegral value I(2θ); a diffraction sensitivity calculation process ofcalculating a diffraction sensitivity I_(C)(ϕ) of the peak originatingfrom the crystal face of graphite by correcting an integrating rangewith the correction coefficient δ and integrating the X-ray diffractionimage with respect to a diffraction angle (2θ); and an orientationdegree calculation process of calculating a fiber orientation degreeSd(β) by the method of Hermans from the diffraction sensitivityI_(C)(ϕ).

In the method for measuring a fiber orientation degree according to thepresent invention, the correction coefficient calculation processincludes calculating the correction coefficient δ by Formula (1) below:δ=(2θ)_(A)−tan⁻¹{(1−t/L)·tan(2θ)_(A)}  (1)

in Expression (1), t indicates a thickness (mm) of the sample, and Lindicates a distance (mm) from an incident plane of the X-ray of thesample to a film surface on which the X-ray diffraction image isprojected. As a matter of course, a size of a film that is used forobtain the diffraction image is larger than L·tan(2ar_(A).

In the method for measuring a fiber orientation degree according to thepresent invention, the diffraction sensitivity calculation processincludes setting an angular integrating range to be from (2θ)_(A)−δ to(2θ)_(A)+δ when (2θ)_(A)+δ>(2θ)_(B) and setting the angular integratingrange to be from (2θ)_(A)−δ to (2θ)_(B) when (2θ)_(A)+δ≤(2θ)_(B).

In the method for measuring a fiber orientation degree according to thepresent invention, the diffraction sensitivity calculated at thediffraction sensitivity calculation process is a sum of diffractionsensitivities of crystal faces [002], [004], and [006] of graphite.

In the method for measuring a fiber orientation degree according to thepresent invention, the orientation degree calculation process includescalculating the fiber orientation degree Sd(β) by Expressions (2), (3),and (4) below:S ₀=∫_(−π/2(−90°)) ^(+π/2(+90°)) I _(C)(ϕ)dϕ  (2)S ₁(β)=∫_(−π/2(−90°)) ^(+π/2(+90°)) I _(C)(ϕ)·cos² βdϕ ₀  (3)in Expression 3, β=ϕ−ϕ₀.Sd(β)=(3·S ₁(β)/S ₀−1)/2  (4)

A fiber orientation degree measurement apparatus according to thepresent invention includes: a diffraction image acquisition unitconfigured to irradiate a sample formed of a composite materialcontaining discontinuous carbon fibers with an X-ray to acquire an X-raydiffraction image; a peak angle calculation unit configured to calculatean angle (2θ)_(A) of a peak originating from a crystal face of graphitefrom an inflection point A of an integral value I(2θ) obtained byintegrating the X-ray diffraction image with respect to an azimuth angle(ϕ); a correction coefficient calculation unit configured to calculate acorrection coefficient δ of a thickness of the sample; an upper limitcalculation unit configured to calculate an upper limit (2θ)_(B) of thepeak of the crystal face of graphite from an inflection point B of theintegral value I(2θ); a diffraction sensitivity calculation unitconfigured to calculate a diffraction sensitivity I_(C)(ϕ) of the peakoriginating from the crystal face of graphite by correcting anintegrating range with the correction coefficient δ and integrating theX-ray diffraction image with respect to a diffraction angle (2θ); and anorientation degree calculation unit configured to calculate a fiberorientation degree Sd(β) by the method of Hermans from the diffractionsensitivity I_(C)(ϕ).

A control program for a fiber orientation degree measurement apparatusaccording to the present invention executes: a diffraction imageacquisition procedure of irradiating a sample formed of a compositematerial containing discontinuous carbon fibers with an X-ray to acquirean X-ray diffraction image; a peak angle calculation procedure ofcalculating an angle (2θ)_(A) of a peak originating from a crystal faceof graphite from an inflection point A of an integral value I(2θ)obtained by integrating the X-ray diffraction image with respect to anazimuth angle (ϕ); a correction coefficient calculation procedure ofcalculating a correction coefficient δ of a thickness of the sample; anupper limit calculation procedure of calculating an upper limit (2θ)_(B)of the peak of the crystal face of graphite from an inflection point Bof the integral value I(2θ); a diffraction sensitivity calculationprocedure of calculating a diffraction sensitivity I_(C)(ϕ) of the peakoriginating from the crystal face of graphite by correcting anintegrating range with the correction coefficient δ and integrating theX-ray diffraction image with respect to a diffraction angle (2θ); and anorientation degree calculation procedure of calculating a fiberorientation degree Sd(β) by the method of Hermans from the diffractionsensitivity I_(C)(ϕ).

Advantageous Effects of Invention

The method for measuring a fiber orientation degree, the fiberorientation degree measurement apparatus, and the control program for afiber orientation degree measurement apparatus of the present inventiondo not need to produce a standard sample, also consider fiberorientation in the thickness direction of the sample, and can thuscalculate the orientation degree of the carbon fibers in CFRP simply andmore accurately.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a fiber orientation degree measurementapparatus according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating acquisition of an X-ray diffractionimage according to the embodiment of the present invention.

FIG. 3 is a diagram of an exemplary X-ray diffraction image according tothe embodiment of the present invention.

FIG. 4 is a diagram of an exemplary diffraction pattern in an azimuthangle (ϕ) of the X-ray diffraction image in FIG. 3.

FIG. 5 is a diagram of a relation between an integral value I(2θ)obtained by integrating the X-ray diffraction image in FIG. 3 withrespect to the azimuth angle (ϕ) and a diffraction angle (2θ).

FIG. 6 is an enlarged view of the part indicated by the dotted line inFIG. 5.

FIG. 7 is a diagram of a relation between a crystal face of graphite anda diffraction angle (2θ) of its peak.

FIG. 8 is an enlarged view of the part indicated by the dotted line inFIG. 5.

FIG. 9 is an enlarged view of the part indicated by the dotted line inFIG. 4.

FIG. 10 is a diagram of a relation between the azimuth angle (ϕ) and adiffraction sensitivity I_(C)(ϕ) originating from the peak of thecrystal face of graphite.

FIG. 11 is a diagram illustrating calculation of a fiber orientationdegree Sd(β) from FIG. 10.

FIG. 12 is a diagram of a relation between the azimuth angle (ϕ) and thefiber orientation degree Sd(β).

FIG. 13 is a flowchart illustrating measurement of the fiber orientationdegree Sd(β) according to the embodiment of the present invention.

DESCRIPTION OF EMBODIMENTS

The following describes a method for measuring a fiber orientationdegree, a fiber orientation degree measurement apparatus, and a controlprogram for a fiber orientation degree measurement apparatus of thepresent invention with reference to the accompanying drawings.

FIG. 1 is a block diagram of a fiber orientation degree measurementapparatus 100 according to an embodiment of the present invention. Thefiber orientation degree measurement apparatus 100 includes adiffraction image acquisition unit 10, a controller 20 controllingunits, and a display unit 30 displaying a measured fiber orientationdegree.

The diffraction image acquisition unit 10 irradiates sample formed of acomposite material containing discontinuous carbon fibers with an X-rayto acquire an X-ray diffraction image (a Debye ring). With measurementof a fiber orientation degree of the discontinuous carbon fibers in thecomposite material as an object, and with CFRP mainly containingdiscontinuous carbon fibers and a matrix resin as a sample, the fiberorientation degree measurement apparatus 100 of the present inventionacquires the X-ray diffraction image using a characteristic X-ray suchas the Cu-Kα line. The fiber orientation degree measurement apparatus100 of the present invention is suitable for measurement of anorientation degree of the discontinuous carbon fibers in CFRP and canalso be used for measurement of a fiber orientation degree in a matformed of discontinuous carbon fibers containing no matrix resin. Thediscontinuous carbon fibers may be any of PAN-based and pitch-basedcarbon fibers. The matrix resin can be the sample of the presentinvention when any of a thermosetting resin, a thermoplastic resin, anda resin containing both a thermosetting resin and a thermoplastic resinis used so long as they are resins used for CFRP.

As illustrated in FIG. 2, the X-ray diffraction image can be acquired byirradiating the sample with an X-ray and receiving the X-ray reflectedon a crystal face of the sample with a film (a camera) or an X-raydetector such as a flat panel detector (FPD). The X-ray diffractionimage can be obtained by irradiating the sample (with a width of 5 to 10mm, a length of 15 to 25 mm, and a thickness of 0.1 to 10 mm) with thecharacteristic X-ray (the Cu-Kα line) for 10 minutes. FIG. 3 is adiagram of an exemplary X-ray diffraction image according to theembodiment of the present invention. FIG. 3 is an X-ray diffractionimage of CFRP containing nylon 6 (polyamide 6) as the matrix resin, inwhich a double ring (a Debye ring) originating from a polyamide crystalis observed (a shadow projected at the lower part of the X-raydiffraction image is a shadow of an apparatus applying the X-ray).

The controller 20 has a peak angle calculation unit 21, a correctioncoefficient calculation unit 22, an upper limit calculation unit 23, adiffraction sensitivity calculation unit 24, and an orientation degreecalculation unit 25. The controller 20 is implemented by using a centralprocessing unit (CPU) executing various kinds of processing programs, aread only memory (ROM) storing therein the various kinds of processingprograms and the like in advance, and a random access memory (RAM)storing therein an arithmetic orientation degree of each processing andthe like. As the controller 20, a general-purpose computer such as awork station or a personal computer can be used.

The peak angle calculation unit 21 extracts a diffraction pattern with acertain azimuth angle (ϕ) from the X-ray diffraction image acquired bythe diffraction image acquisition unit 10 and calculates an angle(2θ)_(A) of a peak originating from a crystal face of graphite from aninflection point of an integral value of the diffraction pattern.

As illustrated in FIG. 2, the X-ray diffraction image indicates arelation between a diffraction angle (2θ) and a diffraction sensitivityI(2θ, ϕ) of the X-ray reflected on the crystal face of the sample, whichis, for example, the polyamide crystal or the crystal face [002], [004],[006], or the like of graphite, and the azimuth angle (ϕ). The peakangle calculation unit 21 calculates the angle (2θ)_(A) of the peakoriginating from the crystal face of graphite from a diffraction patternin a direction of the azimuth angle (ϕ), that is, a diffraction patternin a circumferential direction from the center of the X-ray diffractionimage in the direction of the azimuth angle (ϕ) The following describescalculation of the angle (2θ)_(A) of the peak originating from thecrystal face [002], which gives the highest diffraction sensitivity.

FIG. 4 is a diagram of an exemplary diffraction pattern at the azimuthangle (ϕ) of the X-ray diffraction image in FIG. 3. In the diffractionpattern in FIG. 4, peaks with a diffraction angle (2θ) of around 20° and24.5° originate from the polyamide crystal, whereas a peak of a shoulderof the peak of polyamide around 24.5° is a peak originating from thecrystal face [002] of graphite.

The peak angle calculation unit 21 integrates the X-ray diffractionimage in FIG. 3 in the direction of the azimuth angle (ϕ) according toExpression (5) below to calculate the angle (2θ)_(A) of the peak of thecrystal face [002] of graphite from the inflection point.I(2θ)=∫_(−π/2(−90°)) ^(+π/2(+90°)) I(2θ,ϕ)dϕ  (5)

In Expression (5), the reason why the integrating range is from −π/2(−90°) to +π/2 (+90°) is to exclude the influence of a shadow projectedon the X-ray diffraction image. When no shadow is projected on the X-raydiffraction image depending on the used apparatus, the X-ray diffractionimage may be integrated from −π (−180°) to +π (+180°).

FIG. 5 is a diagram of a relation between an integral value I(2θ)obtained by integrating the X-ray diffraction image in FIG. 3 withrespect to the azimuth angle (ϕ) and the diffraction angle (2θ). FIG. 6is an enlarged view of the part indicated by the dotted line in FIG. 5(near the diffraction angle of the crystal face [002] of graphite). Aninflection point A appearing near the diffraction angle 2θ of thecrystal face [002] of graphite of the integral value I(2θ) illustratedin FIG. 5 is the angle (2θ)_(A) of the peak of the crystal face [002] ofgraphite.

The peak angle (2θ)_(A) originating from the [002] face can bedetermined by referring to the diffraction angle 2θ (25.9 to 26.6°) ofthe crystal face [002] of general graphite illustrated in FIG. 7 andcalculating a differential coefficient from above the diffraction angle2θ (25.9 to 26.6°) of the crystal face [002]. Although the diffractionangle 2θ of the crystal face of graphite varies by conditions when agraphite crystal is generated, the diffraction angle 2θ of the crystalface [002] of the discontinuous carbon fibers used as the sample isconsidered to be near the diffraction angle 2θ(25.9 to 26.6°) of thecrystal face [002] illustrated in FIG. 7, and the inflection point A canbe determined by calculating the differential coefficient near thediffraction angle 2θ(25.9 to 26.6°) of the crystal face [002].

The correction coefficient calculation unit 22 calculates a correctioncoefficient δ of a thickness t (mm) of the sample. The correctioncoefficient δ can be calculated by Expression (1) below.δ=(2θ)_(A)−tan⁻¹{(1−t/L)·tan(2θ)_(A)}  (1)

In Expression (1), t indicates the thickness (mm) of the sample, and Lindicates a distance (mm) from an incident plane of the X-ray of thesample to a film surface on which the X-ray diffraction image isprojected.

The diffraction angle (2θ) on the horizontal axis of the diffractionpattern in FIG. 4 includes information in a direction of the thickness tof the sample, and the peak angle (2θ)_(A) is corrected with thecorrection coefficient δ. With this correction, a fiber orientationdegree with fiber orientation not only in the two-dimensional (in-plane)direction of the sample but also in the thickness direction taken intoaccount can be measured.

The upper limit calculation unit 23 calculates an upper limit (2θ)_(B)of the peak originating from the crystal face of graphite from an angle(2θ)_(B) of an inflection point B of the integral value I(2θ) obtainedby integrating the X-ray diffraction image with respect to the azimuthangle (ϕ). The upper limit (2θ)_(B) of the peak is an upper limit of anintegrating range when the diffraction sensitivity calculation unit 24described below integrates the diffraction sensitivity I(2θ, ϕ) withrespect to the diffraction angle (2θ) to calculate a diffractionsensitivity I_(C)(ϕ) of the peak of the crystal face of graphite.

FIG. 8 is an enlarged view of the part indicated by the dotted line inFIG. 5 (near the angle (2θ)_(A) of the peak of the crystal face [002] ofgraphite). The inflection point B is determined by calculating adifferential coefficient upward from the angle (2θ)_(A) of the peak ofthe crystal face [002] of graphite. The angle (2θ)_(B) of the nextinflection point B above the angle (2θ)_(A) of the peak of the crystalface [002] of graphite (the inflection point following the inflectionpoint A; the differential coefficient of the inflection point B isnormally zero) is the upper limit of the integrating range when thediffraction sensitivity I_(C)(ϕ) is calculated.

The diffraction sensitivity calculation unit 24 calculates thediffraction sensitivity I_(C)(ϕ) of the peak originating from thecrystal face of graphite by correcting the integrating range with thecorrection coefficient δ calculated by the correction coefficientcalculation unit 22 and integrating the X-ray diffraction image withrespect to the diffraction angle (2θ). FIG. 9 is an enlarged view of thepart indicated by the dotted line in FIG. 4. FIG. 9 illustratescalculation of a diffraction sensitivity I₀₀₂(ϕ) originating from thepeak of the crystal face [002] of graphite. In FIG. 9, the shaded partis the diffraction sensitivity I₀₀₂(ϕ); the X-ray diffraction image(diffraction pattern) is integrated to calculate the diffractionsensitivity I₀₀₂(ϕ).

With a value (2θ)_(A)−δ obtained by subtracting the correctioncoefficient δ from the angle (2θ)_(A) of the peak of the crystal face[002] of graphite as the lower limit of the integrating range and with(2θ)_(B) calculated by the upper limit calculation unit 23 as the upperlimit, the peak sensitivity I₀₀₂(ϕ) of the crystal face [002] ofgraphite can be calculated by Expression (6) below.I ₀₀₂(ϕ)=∫_((2θ)) _(A−δ) ^((2θ)) ^(B) I(2θ,ϕ)d(2θ)  (6)

Depending on the correction coefficient δ, a value (2θ)_(A)+δ obtainedby adding the correction coefficient δ to the angle (2θ)_(A) of the peakof the crystal face [002] of graphite may be a value larger than(2θ)_(B). In such a case, the peak sensitivity I₀₀₂(ϕ) of the crystalface [002] of graphite may be calculated by Expression (7) below with(2θ)_(A)−δ as the lower limit and with (2θ)_(A)+δ as the upper limit.I ₀₀₂(ϕ)=∫_((2θ)) _(A−δ) ^((2θ)) ^(A+δ) I(2θ,ϕ)d(2θ)  (7)

The diffraction image acquisition unit 10 illustrated in FIG. 2 canobtain an X-ray diffraction image containing diffraction at the crystalfaces [002], [004], and [006] of graphite, and a diffraction sensitivityI₀₀₄(ϕ) and a diffraction sensitivity I₀₀₆(ϕ) of peaks originating fromthe crystal faces [004] and [006], respectively, of graphite arecalculated in the same manner as the diffraction sensitivity I₀₀₂(ϕ) ofthe peak of the crystal face [002], and the sum of the diffractionsensitivities of the crystal faces of graphite is calculated as thediffraction sensitivity I_(C)(ϕ) from Expression (8) below.I _(C)(ϕ)=I ₀₀₂(ϕ)+I ₀₀₄(ϕ)+I ₀₀₆(ϕ)  (8)

Alternatively, the diffraction sensitivity I₀₀₂(ϕ) at the crystal face[002] of graphite is the largest, and the diffraction sensitivityI₀₀₂(ϕ) may be regarded as the diffraction sensitivity I_(C)(ϕ).

The orientation degree calculation unit 25 calculates the fiberorientation degree Sd(β) by the method of Hermans from the diffractionsensitivity I_(C)(ϕ). FIG. 10 is a diagram of a relation between theazimuth angle (ϕ) and the diffraction sensitivity I_(C)(ϕ) originatingfrom the peak of the crystal face of graphite, in which the diffractionsensitivity I_(C)(ϕ) with an azimuth angle (ϕ) of ϕ=1 to 360° isillustrated (for ϕ=140 to 212°, the diffraction sensitivity I_(C)(ϕ) isnot calculated under the influence of the shadow of the apparatus).

The fiber orientation degree Sd(β) is an indicator indicating a level ofpresence in each direction at which the discontinuous carbon fibers areoriented within the sample and is calculated using Expressions (2), (3),and (4) below by the method of Hermans in the present invention. FIG. 11is a diagram illustrating calculation of the fiber orientation degreeSd(β) from FIG. 10.S ₀=∫_(−π/2(−90°)) ^(+π/2(+90°)) I _(C)(ϕ)dϕ  (2)S ₁(β)=∫_(−π/2(−90°)) ^(+π/2(+90°)) I _(C)(ϕ)·cos² βdϕ ₀  (3)

In Expression (3), β=ϕ−ϕ₀.Sd(β)=(3·S ₁(β)/S ₀−1)/2  (4)

As shown in Expression (9) below, a maximum value Sd₀ of Sd(β)determined by Expression (4) is a fiber orientation degree Sd₀ of thesample.Sd ₀=max·Sd(β)  (9)

As shown in Expression (10) below, β when Sd(β) is the maximum value Sd₀is β₀.β₀=β|max·Sd(β)  (10)

The crystal faces [002] and the like of graphite deviate from thedirection of a principal axis of the carbon fibers by 90°, and aprincipal orientation angle α₀ of the discontinuous carbon fibers is asExpression (11) below.α₀=β₀±π/2  (11)

FIG. 12 is a diagram of a relation between the azimuth angle (ϕ) and thefiber orientation degree Sd(β). The fiber orientation degree Sd(β) isillustrated together with the diffraction sensitivity I₀₀₂(ϕ), in whichthe data of the fiber orientation degree Sd(β) and the diffractionsensitivity I₀₀₂(ϕ) in ϕ=90 to 270° is illustrated as rotationalsymmetry of the data in 0 to 90° and 270 to 360° for the sake ofsimplicity. It can be seen from the fiber orientation degree Sd(β) inFIG. 12 that the maximum value Sd₀ is given by β₀=358°, whereas theprincipal orientation angle α₀ is 88°.

The fiber orientation degree Sd(β) of the discontinuous carbon fibers inthe sample is measured by the process of a flowchart illustrated in FIG.13.

First, the diffraction image acquisition unit 10 acquires an X-raydiffraction image of the sample (Step S1), and the peak anglecalculation unit 21 calculates the angle (2θ)_(A) of the peakoriginating from the crystal face of graphite from the inflection pointA of the integral value I(2θ) obtained by integrating the X-raydiffraction image with respect to the azimuth angle (ϕ) (Step S2). Thecrystal face of graphite for which the angle (2θ)_(A) is calculated maybe [002], [004], and [006] or only [002].

Subsequently, the correction coefficient calculation unit 22 calculatesthe correction coefficient δ of the thickness of the sample (Step S3).The correction coefficient δ may be calculated from Expression (2).

Subsequently, the upper limit calculation unit 23 calculates the upperlimit (2θ)_(B) of the peak of the crystal face of graphite from theinflection point B of the integral value I(2θ) obtained by integratingthe X-ray diffraction image with respect to the azimuth angle (ϕ) (StepS4). The inflection point B is a next inflection point above the angle(2θ)_(A) of the peak originating from the crystal face of graphite.

After the upper limit (2θ)_(B) of the peak is calculated (Step S4), thediffraction sensitivity calculation unit 24 corrects the integratingrange with the correction coefficient δ calculated at Step S3 (Step S5)and integrates the X-ray diffraction image with the integrating rangecalculated at Step S5 to calculate the diffraction sensitivity I_(C)(ϕ)of the peak originating from the crystal face of graphite (Step S6). Theintegrating range is from (2θ)_(A)−δ to (2θ)_(B) when(2θ)_(B)≥(2θ)_(A)+δ and from (2θ)_(A)−δ to (2θ)_(B) when(2θ)_(B)<(2θ)_(A)+δ.

After the diffraction sensitivity I_(C)(ϕ) is calculated (Step S6), theorientation degree calculation unit 25 calculates the fiber orientationdegree Sd(β) by the method of Hermans from the diffraction sensitivityI_(C)(ϕ) (Step S7). The orientation degree calculation unit 25 outputsthe maximum value Sd₀ of the fiber orientation degree Sd(β) and theprincipal orientation angle α₀ to the controller 20.

The controller 20 performs control to display the maximum value Sd₀ ofthe fiber orientation degree Sd(β) and the principal orientation angleα₀ on the display unit 30 (Step S8).

The present invention uses Expression (8) so that fiber orientation notonly in the in-plane direction of the sample but also in the directionof the thickness t is taken into account for calculation of the fiberorientation degree Sd(β). With this consideration, the fiber orientationdegree Sd(β) of a sample in which fiber orientation varies in thedirection of the thickness t can be measured more accurately.

REFERENCE SIGNS LIST

-   -   10 Diffraction image acquisition unit    -   20 Controller    -   21 Peak angle calculation unit    -   22 Correction coefficient calculation unit    -   23 Upper limit calculation unit    -   24 Diffraction sensitivity calculation unit    -   25 Orientation degree calculation unit    -   30 Display unit    -   100 Fiber orientation degree measurement apparatus

The invention claimed is:
 1. A method for measuring a fiber orientationdegree comprising: a diffraction image acquisition process ofirradiating a sample formed of a composite material containingdiscontinuous carbon fibers with an X-ray to acquire an X-raydiffraction image; a peak angle calculation process of calculating anangle (2θ)_(A) of a peak originating from a crystal face of graphitefrom an inflection point A of an integral value I(2θ) obtained byintegrating the X-ray diffraction image with respect to an azimuth angle(ϕ); a correction coefficient calculation process of calculating acorrection coefficient δ of a thickness of the sample; an upper limitcalculation process of calculating an upper limit (2θ)_(B) of the peakof the crystal face of graphite from an inflection point B of theintegral value I(2θ); a diffraction sensitivity calculation process ofcalculating a diffraction sensitivity I_(C)(ϕ) of the peak originatingfrom the crystal face of graphite by correcting an integrating rangewith the correction coefficient δ and integrating the X-ray diffractionimage with respect to a diffraction angle (2θ); and an orientationdegree calculation process of calculating a fiber orientation degreeSd(β) by the method of Hermans from the diffraction sensitivityI_(C)(ϕ), wherein the correction coefficient calculation processincludes calculating the correction coefficient δ by Formula (1) below:δ=(2θ)_(A)−tan⁻¹{(1−t/L)·tan(2θ)_(A)}  (1) in Expression (1), tindicates a thickness (mm) of the sample, and L indicates a distance(mm) from an incident plane of the X-ray of the sample to a film surfaceon which the X-ray diffraction image is projected.
 2. The method formeasuring a fiber orientation degree according to claim 1, wherein thediffraction sensitivity calculation process includes setting an angularintegrating range to be from (2θ)_(A)−δ to (2θ)_(A)+δ when(2θ)_(A)+δ>(2θ)_(B) and setting the angular integrating range to be from(2θ)_(A)−δ to (2θ)_(B) when (2θ)_(A)+δ≤(2θ)_(B).
 3. The method formeasuring a fiber orientation degree according to claim 1, wherein thediffraction sensitivity calculated at the diffraction sensitivitycalculation process is a sum of diffraction sensitivities of crystalfaces [002], [004], and [006] of graphite.
 4. The method for measuring afiber orientation degree according to claim 1, wherein the orientationdegree calculation process includes calculating the fiber orientationdegree Sd(β) by Expressions (2), (3), and (4) below:S ₀=∫_(−π/2(−90°)) ^(+π/2(+90°)) I _(C)(ϕ)dϕ  (2)S ₁(β)=∫_(−π/2(−90°)) ^(+π/2(+90°)) I _(C)(ϕ)·cos² βdϕ ₀  (3) inExpression 3, β=ϕ−ϕ₀,Sd(β)=(3·S ₁(β)/S ₀−1)/2  (4).
 5. A fiber orientation degree measurementapparatus comprising: an X-ray diffraction imaging system including anX-ray irradiator configured to irradiate a sample formed of a compositematerial containing discontinuous carbon fibers with an X-ray to acquirean X-ray diffraction image; and a CPU programmed to function as: a peakangle calculation unit configured to calculate an angle (2θ)_(A) of apeak originating from a crystal face of graphite from an inflectionpoint A of an integral value I(2θ) obtained by integrating the X-raydiffraction image with respect to an azimuth angle (ϕ); a correctioncoefficient calculation unit configured to calculate a correctioncoefficient δ of a thickness of the sample; an upper limit calculationunit configured to calculate an upper limit (2θ)_(B) of the peak of thecrystal face of graphite from an inflection point B of the integralvalue I(2θ); a diffraction sensitivity calculation unit configured tocalculate a diffraction sensitivity I_(C)(ϕ) of the peak originatingfrom the crystal face of graphite by correcting an integrating rangewith the correction coefficient δ and integrating the X-ray diffractionimage with respect to a diffraction angle (2θ); and an orientationdegree calculation unit configured to calculate a fiber orientationdegree Sd(β) by the method of Hermans from the diffraction sensitivityI_(C)(ϕ), wherein the CPU is further configured to calculate thecorrection coefficient δ by Formula (1) below:δ=(2θ)_(A)−tan⁻¹{(1−t/L)·tan(2θ)_(A)}  (1) in Expression (1), tindicates a thickness (mm) of the sample, and L indicates a distance(mm) from an incident plane of the X-ray of the sample to a film surfaceon which the X-ray diffraction image is projected.
 6. A non-transitorycomputer-readable recording medium with an executable program storedthereon, the program being a control program for a fiber orientationdegree measurement apparatus executing: a diffraction image acquisitionprocedure of irradiating a sample formed of a composite materialcontaining discontinuous carbon fibers with an X-ray to acquire an X-raydiffraction image; a peak angle calculation procedure of calculating anangle (2θ)_(A) of a peak originating from a crystal face of graphitefrom an inflection point A of an integral value I(2θ) obtained byintegrating the X-ray diffraction image with respect to an azimuth angle(ϕ); a correction coefficient calculation procedure of calculating acorrection coefficient δ of a thickness of the sample; an upper limitcalculation procedure of calculating an upper limit (2θ)_(B) of the peakof the crystal face of graphite from an inflection point B of theintegral value I(2θ); a diffraction sensitivity calculation procedure ofcalculating a diffraction sensitivity I_(C)(ϕ) of the peak originatingfrom the crystal face of graphite by correcting an integrating rangewith the correction coefficient δ and integrating the X-ray diffractionimage with respect to a diffraction angle (2θ); and an orientationdegree calculation procedure of calculating a fiber orientation degreeSd(β) by the method of Hermans from the diffraction sensitivityI_(C)(ϕ), wherein the correction coefficient calculation procedureincludes calculating the correction coefficient δ by Formula (1) below:δ=(2θ)_(A)−tan⁻¹{(1−t/L)·tan(2θ)_(A)}  (1) in Expression (1), tindicates a thickness (mm) of the sample, and L indicates a distance(mm) from an incident plane of the X-ray of the sample to a film surfaceon which the X-ray diffraction image is projected.